Control for Schrödinger operators on 2-tori: rough potentials
Jean Bourgain
Institute for Advanced Study, Princeton, United StatesNicolas Burq
Université Paris-Sud, Orsay, FranceMaciej Zworski
University of California, Berkeley, USA
Abstract
For the Schrödinger equation, on a torus, an arbitrary non-empty open set provides control and observability of the solution: . We show that the same result remains true for where , and is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for and conjectured for . The higher dimensional generalization remains open for
Cite this article
Jean Bourgain, Nicolas Burq, Maciej Zworski, Control for Schrödinger operators on 2-tori: rough potentials. J. Eur. Math. Soc. 15 (2013), no. 5, pp. 1597–1628
DOI 10.4171/JEMS/399